Must a criminal suspect "unequivocably" ask for counsel?

To summarize: The police badger a suspect into a confession. During the interrogation, they prevent him from asking for counsel by interrupting him whenever he is about to ask. The prosecutor then argues that the suspect was required to "unequivocally" ask for counsel.

Does anyone see anything wrong with this?

Police are in a position of power in the interrogation room, and it is very easy to press suspects into going along with what the police want, even, in some cases, when the person is innocent. That's the reason we have the "right of counsel." Police should not be allowed to prevent suspects from invoking this right simply by cutting them off whenever the suspects start to say they want an attorney.